Matches in SemOpenAlex for { <https://semopenalex.org/work/W2999433565> ?p ?o ?g. }
Showing items 1 to 69 of
69
with 100 items per page.
- W2999433565 abstract "In this thesis we develop a functional analytic framework for shape optimization with elliptic partial differential equation (PDE) constraints in classical function spaces (Holder spaces). This approach is motivated by shape optimization problems, which are subjected to linear elasticity constraints and involve a special class of shape functionals which calculate the failure rate of a mechanically loaded device w.r.t. the component shape. These objectives are ill-defined for H1-solutions of the state equation and the shape derivatives are not defined for H1-material derivatives. Thus, the resulting optimal reliability problems can not be solved by the already existing methods of shape calculus. We develop a general concept on Banach and Hilbert spaces which is based on parameter depending variational equations, classical PDE Solutions, Schauder estimates and compact embeddings and which allows to transfer differentiability in lower Banach space topologies to higher ones. We apply this framework to the linear elasticity equation and its variational formulation, given that the domain is transformed according to the speed method. We prove the existence of material and local shape derivatives in Holder spaces, the existence of shape derivatives and derive adjoint equations. We also give a classification of the L2-shape gradient w.r.t. its regularity and its potential to sustain the domain regularity along a descent flow." @default.
- W2999433565 created "2020-01-23" @default.
- W2999433565 creator A5084584954 @default.
- W2999433565 date "2020-03-05" @default.
- W2999433565 modified "2023-09-24" @default.
- W2999433565 title "On Shape Calculus with Elliptic PDE Constraints in Classical Function Spaces" @default.
- W2999433565 doi "https://doi.org/10.25926/pkfr-kr55" @default.
- W2999433565 hasPublicationYear "2020" @default.
- W2999433565 type Work @default.
- W2999433565 sameAs 2999433565 @default.
- W2999433565 citedByCount "3" @default.
- W2999433565 countsByYear W29994335652020 @default.
- W2999433565 crossrefType "posted-content" @default.
- W2999433565 hasAuthorship W2999433565A5084584954 @default.
- W2999433565 hasConcept C121332964 @default.
- W2999433565 hasConcept C132954091 @default.
- W2999433565 hasConcept C134306372 @default.
- W2999433565 hasConcept C135628077 @default.
- W2999433565 hasConcept C142730499 @default.
- W2999433565 hasConcept C202444582 @default.
- W2999433565 hasConcept C202615002 @default.
- W2999433565 hasConcept C28826006 @default.
- W2999433565 hasConcept C29513896 @default.
- W2999433565 hasConcept C33923547 @default.
- W2999433565 hasConcept C36503486 @default.
- W2999433565 hasConcept C62799726 @default.
- W2999433565 hasConcept C93779851 @default.
- W2999433565 hasConcept C97355855 @default.
- W2999433565 hasConceptScore W2999433565C121332964 @default.
- W2999433565 hasConceptScore W2999433565C132954091 @default.
- W2999433565 hasConceptScore W2999433565C134306372 @default.
- W2999433565 hasConceptScore W2999433565C135628077 @default.
- W2999433565 hasConceptScore W2999433565C142730499 @default.
- W2999433565 hasConceptScore W2999433565C202444582 @default.
- W2999433565 hasConceptScore W2999433565C202615002 @default.
- W2999433565 hasConceptScore W2999433565C28826006 @default.
- W2999433565 hasConceptScore W2999433565C29513896 @default.
- W2999433565 hasConceptScore W2999433565C33923547 @default.
- W2999433565 hasConceptScore W2999433565C36503486 @default.
- W2999433565 hasConceptScore W2999433565C62799726 @default.
- W2999433565 hasConceptScore W2999433565C93779851 @default.
- W2999433565 hasConceptScore W2999433565C97355855 @default.
- W2999433565 hasLocation W29994335651 @default.
- W2999433565 hasOpenAccess W2999433565 @default.
- W2999433565 hasPrimaryLocation W29994335651 @default.
- W2999433565 hasRelatedWork W1547917734 @default.
- W2999433565 hasRelatedWork W1977429573 @default.
- W2999433565 hasRelatedWork W1994381581 @default.
- W2999433565 hasRelatedWork W2004778474 @default.
- W2999433565 hasRelatedWork W2019907348 @default.
- W2999433565 hasRelatedWork W2030969737 @default.
- W2999433565 hasRelatedWork W2113823326 @default.
- W2999433565 hasRelatedWork W2138663546 @default.
- W2999433565 hasRelatedWork W2464779483 @default.
- W2999433565 hasRelatedWork W2736722776 @default.
- W2999433565 hasRelatedWork W2891731318 @default.
- W2999433565 hasRelatedWork W2952147368 @default.
- W2999433565 hasRelatedWork W2962712082 @default.
- W2999433565 hasRelatedWork W3012324347 @default.
- W2999433565 hasRelatedWork W3023289317 @default.
- W2999433565 hasRelatedWork W3043576762 @default.
- W2999433565 hasRelatedWork W3102743179 @default.
- W2999433565 hasRelatedWork W313791767 @default.
- W2999433565 hasRelatedWork W3206918464 @default.
- W2999433565 hasRelatedWork W332428766 @default.
- W2999433565 isParatext "false" @default.
- W2999433565 isRetracted "false" @default.
- W2999433565 magId "2999433565" @default.
- W2999433565 workType "article" @default.